1. Field of the Disclosure
The present disclosure relates to a method and apparatus for determining a scattered wave particle velocity for imaging a formation.
2. Description of the Related Art
In borehole acoustic logging-while-drilling and wireline logging, there is an ever increasing demand for imaging structural features in a formation away from a borehole. Imaging is an inversion process, based on an inverse model which aims at reconstructing contrasts in medium parameters related to structural features of the formation from a known or measured scattered wavefield which finds its origin at points located in the formation. The scattered wavefield results from an interaction of an incident wavefield with the structural feature (scatterer). The incident wavefield is generated by known sources, which in case of a borehole acoustic logging-while-drilling or wireline configuration are typically located on a borehole tool surrounded by borehole fluid. Associated with the inverse model is a forward model that predicts the scattered wavefield given a known contrast in medium parameters. An actual measurement in the borehole of pressure and/or particle velocity, for example, provides a total wave field that is the sum of the incident wavefield and scattered wavefield. Current methods (e.g., Finite Difference, Finite Elements) for calculating the total wavefield are time-intensive, since these methods require the calculation of a new model at each location of the borehole tool in the borehole. The present disclosure provides a method that reduces the computational burden for calculating incident and scattered wavefields.